Refined Iterative Methods for Computation of the Solution and the Eigenvalues of Self-Adjoint Boundary Value Problems

I: The Self-Adjoint Boundary Value Problem.- 1. Problems of Dirichlet’s and Poisson’s type.- 2. Better approximations.- 3. Energy on the boundary.- 4. Eigenvalue problems.- 5. Biharmonic problems.- 6. Adaption for practical purposes; the test example.- 7. Modes of oscillation of the plate.- II: Theory of Gradient Methods.- 1. Introduction.- 2. The residual polynomial.- 3. Methods with two-term recursive formulae.- 4. Methods with three-term recursive formulae.- 5. Combined methods.- 6. The cgT-method.- 7. Determination of eigenvalues.- III: Experiments on Gradient Methods.- 1. Introduction.- 2. Survey of the plate experiments.- 3. Solution of the system A x + b = 0 (Plate problem with coarse grid).- 4. Determination of the eigenvalues of A.- 5. Solution of the system A x + b =0 and determination of the eigenvalues of A; fine grid.- 6. Second test example: the bar problem.- 7. Appendix: The first three eigenvectors of A.- IV: Overrelaxation.- 1. Theory.- 2. Numerical results (Plate problem).- 3. The bar problem.- V: Conclusions.- 1. The plate problem.- 2. The bar problem.- 3. Computation of eigenvalues.- 4. Recollection of the facts.- References.